van Arkel-Ketelaar Triangles of Bonding
The chemical elements and binary compounds hold a special place in chemical understanding because they exhibit only a single type of strong chemical bond, of which there are three extreme types: ionic, metallic & covalent:
The Main Group Elements as Materials
The first 36 main group elements are well known materials that can be classified as: metals, metalloids and non-metals:
As materials the chemical elements can only undergo allotopic phase-change processes:
There are 36 main group elements and there are approximately 650 binary (dielemental) compounds (chemical substances) materials that are derived from the first 36 main group elements.
Compounds can be predicted using a combinatorial matrix (interaction table) of main group elements (a type of Karnaugh map):
William B. Jensen's paper: Logic, History, and the Chemistry Textbook, J.Chem.Educ., 817-828, 75, 1998 discusses Grimm’s "Dreieckeschema" from 1928 which uses the logic discussed above:
Fernelius & Robey’s 1935 Bond-Type Triangle
Also in Jensen's paper is a mention of Fernelius & Robey’s Bond-Type Triangle, Fernelius, W.C. and Robey, R.F. The Nature of the Metallic State. J. Chem. Educ. 1935, 12, 53–68:
van Arkel's 1941 Triangle
Van Arkel recognised three extreme material and associated bonding types: ionic, metallic and covalent, and he placed these are the corners of an equilateral triangle. He then suggested intermediate species: for example, carbontetrafluoride, CF4, which has C-F bonds that are intermediate between ionic and covalent and are polar covalent. (We will be exploring these intermediate species further, particularly on the next page, here.)
The beauty of the van Arkel analysis is that real chemical species are used to provide hard empirical evidence. The triangle maps material type to theories of chemical structure.
Ketelaar's 1947 Triangle
van Arkel's idea was developed by Ketelaar, another Dutchman:
Triangle from the Main Group Interaction Matrix
A triangle of bonding is obtained from main group element interactions, above:
Triangle Rotations & Reflections
It transpires that the idea of a "triangle of bonding" with metallic, ionic and covalent extremes is very rich, and it can be extended in many ways.
Geometrically, there are six ways to construct triangles through rotation and reflection:
The original van Arkel triangle is CIM, the Ketelaar triangle is CMI, the main group element interaction matrix triangle is IMC,but it is more convenient to use the MIC formulation.
The Jolly Triangle
It is also possible to select different combinations of species to represent metallic, ionic, covalent and intermediate material types. In his 1985 book, William Jolly gives a triangle of bonding with his own selection of species, a CMI formulation:
Allen's Quantitative Triangle
The Allen triangle of bonding (1992) uses configuration energy (CE): "the average one-electron valence shell energy of the ground-state free atom" as an atomic parameter. CE is used directly to quantify the metal-covalent edge, and the difference in CE is used as a measure of ionic bonding.
The Allen triangle of bonding is restricted to period 3 elements.
William Jensen reviewed the van Arkel-Ketelaar triangle literature in his 1995 paper: J.Chem.Educ. 395-398, 72, 1995. The paper introduces a triangle of bonding quantified in two dimensions using electronegativity data.
The Quantified Jensen Triangle of Bonding uses an electronegativity scale introduced by Martynov & Batsanov. There are two versions, the first used compounds and the second bonds:
A version of the Jensen triangle using (revised) Pauling electronegativity, is reproduced below for the 481 main group binaries. (Only 31 of the first 36 main group elements have electronegativity data.) This diagram is captured from an Excel spreadsheet, and the original .xls file can be downloaded here.
Norman's Quantitative Triangle
N.C. Norman developed a triangle of bonding that, rather like the Allen version, is quantitative in two dimensions and which (like Jensen) uses electronegativity. However, and very confusingly(!), the Norman Triangle of Bonding uses Allen electronegativity rather than Martynov & Batsanov or revised Pauling electronegativity. And yes, it is the same Allen who uses configuration energy rather than electronegativity.
The astute reader will have noticed how similar the Allen configuration energy (CE) triangle is to the Jensen, Norman and other electronegativity triangles of bonding.
MRL's Quantitative Triangle
My personal take on the van Arkel-Ketelaar triangle is to use a single period, for example: Li to F, and to quantify the ionic-covalent edge in terms of % ionic (or covalent) character using electronegativity data and the Pauling equation:
While the % ionic-covalent character numbers are useful and they certainly do seem to be a good indication of polarity and reactivity not too much should be read into them.
Electrical Conductivity: Metallic Bonding
In his 1995 paper, Jensen pointed out that it is possible to explore the metallic region of the van Arkel-Keteleaar triangle using a simple "probe, battery, buzzer" conductivity test. Materials within the area shown below are "conducting" to this simple test, materials outside are "insulating".
Jensen also points out that "Zintl phases", Wikipedia, can be mapped triangle of bonding. Known since the 1930's, "Zintl phases" are formed in liquid ammonia. Zintl phases on the web can be found here.
Heyes' Version of Ketelaar's Triangle
From the website of Dr S.J. Heyes, University of Oxford:
Stephen Lower's Virtual Textbook Version
Triangle of Alchemical "Principles"
Ed Lisic, Professor of Chemistry at the Tennessee Tech University, made contact and wrote: "Mercury, sulfur and salt are the three alchemical "principles" and they fit perfectly into a van Arkel-Ketelaar triangle. Sulfur is for fiery aspect, salt is for earth, and mercury is for the flowing liquid aspect. Sulfur, or covalent would be red, Ionic would be yellow or green, and metallic would be blue."
On this page little has been said about the materials intermediate between:
© Mark R. Leach 1999-
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